what is the difference of two squares rule or formula?

Answer 1

the formula is that
x^2-y^2=(x+y)*(x-y)

Answer 2

The difference of two squares rule is that if you have an equation in which one square is subtracted from another square, you can factor it so that one second term is positive, the other negative:
x^2-y^2 = (x+y)(x-y)
When you recombine them, you get the original equation:
(x+y)(x-y) = x^2 +xy -xy -y^2 = x^2-y^2.

On the other hand with the sum of two squares, such as x^2+y^2, you cannot factor it in the same way and then recombine the factors to return to your original equation. Consider:
x^2+y^2 = (x+y)(x+y)
Now recombine them:
(x+y)(x+y) = x^2+xy+y+y^2 = x^2 + 2xy + y^2.
Thus x^2+y^2 is said to be unfactorable (at least for a beginning algebra student, I won't know for sure for a couple years).

Good luck!

I hope this helps

Answer 3

if you had

a^2 - b^2

if would always equal

(a-b) x (a+b)

which would be the difference of two squares

Answer 4

ax^2 - by^2 = (sqrt(a)x - sqrt(b)y)(sqrt(a)x + sqrt(b)y)

if its x^2 - y^2, then this would be (x - y)(x + y)

if its ax^2 - b, then just leave out the y's in the top answer.